Question: Solve for $x$ : $x^2 - 2x - 35 = 0$
The coefficient on the $x$ term is $-2$ and the constant term is $-35$ , so we need to find two numbers that add up to $-2$ and multiply to $-35$ The two numbers $5$ and $-7$ satisfy both conditions: $ {5} + {-7} = {-2} $ $ {5} \times {-7} = {-35} $ $(x + {5}) (x {-7}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 5) (x -7) = 0$ $x + 5 = 0$ or $x - 7 = 0$ Thus, $x = -5$ and $x = 7$ are the solutions.